Soooooooooo - Indeed Yonni placed the players so that each player plays each power once. However, this combination yields on average each player will play 9 other players multiple times, mostly twice, but a handful 3 times, and not play on average 8 other players.

Because of the interdependencies I do not think the simple math bears out -- there will be more repeats with a smaller pool of players. Extending the number of players will alleviate that for sure.

I agree with Yonni to use the 49 player format so each player only plays another player once, while not playing everyone. Though solving the riddle is quite enticing.

I do not have access to a decent solver - having to make due with Solver in excel which blows big fat chunks. I modeled it, but cannot get Solver to solve it! Happy to share the excel and see if someone else can figure out the missing piece.

We should be able to get a more efficient distribution of multi-plays, but Excel Add-in won't cut it.

By the way, I am happy to play with the heats as is, as to me it is most important to play each power once. We can probably clean out the three time ones manually (MANUALLY -- ughhh, that word gives me the chills...). Though a better solver would SOLVE this.

Damn, I was worried that was going to be the case. The program didn't look that advanced and I didn't double check any of it.

goldfinger PM'ed me over on Vdip, and asked if I was interested in joining. Seems I'm too late for the party?

Potentially, but either way, the more alternates the better.

If it helps, my last GR was 353.56 (from Aug 2011), which would put me at #24 on the current GhostRanking from January 2013.

drano - you're welcome to join.

Thanks jos....You saved me a whole lot of time there. I was reaching the same conclusion though. After 4 rounds people were already having 2-4 repeat opponents. It could be gone through manually though. You'll have to show me this solver in excel, because I've been inputting all the values into a 42x42 matrix manually. I already have a 49 player setup, so you don't have to worry about that.

What happens if we do 49 players but only 7 games?

@GF: I won't be able to start before Monday the 18th of February. Just letting you know!

You might get the tournament seeded and kicked off before I'm done, but I've made progress creating a (terrible, brute-force) algorithm for figuring out the optimal number of players for a multi-player tournament, with a variable number of players per game.

I'm using JavaScript and QUnit. So far my unit tests pass for the simple scenarios (3 players minimum for a 2 player game, etc), but my (ugly, horrible) brute force method doesn't work for the 678+ billion arrays needed to figure out 49 players in a 7 player game.

I'll make it more elegant this weekend. Getting close. Will keep you posted.

Somebody PM me if you have a web server you'd be willing to host a static html page on, for the purpose of sharing this when I'm done.

I can tell you that the 2009-10 TMG Masters Tournament had 8 rounds, 49 players and no repeats during the first 7 rounds. How theGhostMaker set that up I have no idea, but it might be worth giving him a shout out. I believe he has contact info on his profile visible to everyone.

I have the same setup, jmo. I derived it by going through every single game already played in the past Masters and working forward from there as best I could. But if we bump it up to 49 players, we should have no problem with a 7 or 8 round tournament.

Thanks for the work you're putting into this Charlie. Is it okay that I list you as a sitter?

I think Charlie should play. He's one of the best press communicators we have on this site.

I agree with you, Mapu. Its Charlie that's not cooperating with us.

Aww shucks, guys.

@GF - manually input into a 42 x 42 grid ... reading that caused me physical pain, bud. I'll reach out by PM - pretty easy to check matching. Please send me the 49 set, and maybe we can extend it to a higher multiple of 7... does this involve a champion round following the first go results?

No, the winner is decided after the 7 rounds. Solos are worth 1 point, everything else worth 0. Ties are broken based off of strength of schedule (who you soloed against).

I can't tell you how excited I am for this new round. My last Masters experience......I don't think a single game lasted less than 5 months.

Man, this is a tough crowd and that's a tough scoring system. I'm suddenly terrified I'm going to end with zero points.

Statistically, most will Stackelberg

@Stack, most of us do.

49 players is also much easier (apologies if the forum destroys my nice formatting):
Round 1:
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
36 37 38 39 40 41 42
43 44 45 46 47 48 49

Round 2:
1 9 17 25 33 41 49
8 16 24 32 40 48 7
15 23 31 39 47 6 14
22 30 38 46 5 13 21
29 37 45 4 12 20 28
36 44 3 11 19 27 35
43 2 10 18 26 34 42

Round 3:
1 16 31 46 12 27 42
8 23 38 4 19 34 49
15 30 45 11 26 41 7
22 37 3 18 33 48 14
29 44 10 25 40 6 21
36 2 17 32 47 13 28
43 9 24 39 5 20 35

Round 4:
1 23 45 18 40 13 35
8 30 3 25 47 20 42
15 37 10 32 5 27 49
22 44 17 39 12 34 7
29 2 24 46 19 41 14
36 9 31 4 26 48 21
43 16 38 11 33 6 28

Round 5:
1 30 10 39 19 48 28
8 37 17 46 26 6 35
15 44 24 4 33 13 42
22 2 31 11 40 20 49
29 9 38 18 47 27 7
36 16 45 25 5 34 14
43 23 3 32 12 41 21

Round 6:
1 37 24 11 47 34 21
8 44 31 18 5 41 28
15 2 38 25 12 48 35
22 9 45 32 19 6 42
29 16 3 39 26 13 49
36 23 10 46 33 20 7
43 30 17 4 40 27 14

Round 7:
1 44 38 32 26 20 14
8 2 45 39 33 27 21
15 9 3 46 40 34 28
22 16 10 4 47 41 35
29 23 17 11 5 48 42
36 30 24 18 12 6 49
43 37 31 25 19 13 7

Round 8 (optional):
1 8 15 22 29 36 43
2 9 16 23 30 37 44
3 10 17 24 31 38 45
4 11 18 25 32 39 46
5 12 19 26 33 40 47
6 13 20 27 34 41 48
7 14 21 28 35 42 49

Countries can be assigned by merely assigning each column a different country each round, as all players will be in the same column each round except for eight. You can obfuscate by mixing the rounds around and not identifying which round is which when you start games simultaneously.

Hush now, I love the enthusiasm, but you're not supposed to know who everyone else is playing! I already got the 49 covered. I'm gonna use a scrambled version of that, yes.

Does anyone remember who the past winners were?

It would be pretty hard to reverse engineer the schedule and figure out who anyone is. By round 4 or 5, maybe you'd know France from one of your games couldn't be Austria in your current game, or something like that, but that's about as much as you could infer, as far as I can see. It doesn't seem like that comes close to making the games non-anon.

I think goldfinger's saying that it would be pretty easy if he were to use the player order he had listed above. You can know at any point that France from another game isn't Austria from your current game, but that's because there are no repeated players until round 8.

Ah, yeah, I forgot we were back to a world with no repeat players. Yeah, I see why the order in which we start games needs to be scrambled.

No points allowed for draws in The Masters?!?

Wow! I'll have to change the way I'm playing things out in-game a little bit. CRAP! ;0)

That no draws thing is going to change everything drastically...

That's the way it's always been...

It just makes things more cutthroat and less "let's play for the safe draw." It also removes the incentive to kill people off at the end for a smaller draw.